Alternate Definitions for von Zeipel theorem

A theorem that establishes a relation between the radiative flux at some colatitude on the surface of a rotating star and the local effective gravity (which is a function of the angular velocity and colatitude). For a rotating star in which centrifugal forces are not negligible, the equipotentials where gravity, centrifugal force, and pressure are balanced will no longer be spheres. The theorem states that the radiative flux is proportional to the local effective gravity at the considered colatitude, F(θ) ∝ g_eff (θ)α, where α is the gravity darkening coefficient. As a consequence, the stellar surface will not be uniformly bright, because there is a much larger flux and a higher effective temperature at the pole than at the equator (T_eff (θ) ∝ g_eff (θ)β, where β is the gravity darkening exponent. In massive stars this latitudinal dependence of the temperature leads to asymmetric mass loss and also to enhanced average mass loss rates.